Two Proofs of a Conjecture of Amdeberhan, Andrews and Ballantine for double Lambert series and a new Representation for $E_2(q)$

Su-Ping Cui, Rahul Kumar, Aman Singh

In this note, we prove a recent conjecture of Amdeberhan, Andrews and Ballantine concerning a double Lambert series (\textit{J. Combin. Theory Series A} \textbf{221} (2026), Paper…